# Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?

## TL;DR

This paper investigates whether simplified models can accurately measure noise in gene networks, finding that accuracy depends on the half-lives of mRNA and protein.

## Contribution

The study provides new insights into the accuracy of stochastic QSSA models for intrinsic noise quantification in gene regulatory networks.

## Key findings

- Stochastic QSSA models perform better for protein-level noise with varied mRNA and protein half-lives.
- Accuracy for mRNA-level noise is limited to specific half-life combinations.
- Abundance levels of mRNA and protein have minimal impact on model accuracy comparisons.

## Abstract

Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.